We present the first simultaneous photometric and spectroscopic investigation of a large set of RR Lyrae variables in a globular cluster. The radial-velocity data presented comprise the largest sample of RVs of RR Lyrae stars ever obtained. The target is M3; $BVI_{\mathrm{C}}$ time-series of 111 and $b$ flux data of further 64 RRab stars, and RV data of 79 RR Lyrae stars are published. Blazhko modulation of the light curves of 47 percent of the RRab stars are detected. The mean value of the center-of-mass velocities of RR Lyrae stars is $-146.8$ km s$^{-1}$ with 4.52 km s$^{-1}$ standard deviation, which is in good agreement with the results obtained for the red giants of the cluster. The ${\Phi_{21}}^{\mathrm RV}$ phase difference of the RV curves of RRab stars is found to be uniformly constant both for the M3 and for Galactic field RRab stars; no period or metallicity dependence of the ${\Phi_{21}}^{\mathrm RV}$ is detected. The Baade-Wesselink distances of 26 non-Blazhko variables with the best phase-coverage radial-velocity curves are determined; the corresponding distance of the cluster, $10480\pm210$ pc, agrees with the previous literature information. A quadratic formula for the $A_{\mathrm{puls}}-A_V$ relation of RRab stars is given, which is valid for both OoI and OoII variables. We also show that the $(V-I)_0$ of RRab stars measured at light minimum is period dependent, there is at least 0.1 mag difference between the colours at minimum light of the shortest- and longest-period variables.